Metamathematical Properties of Intuitionistic Set Theories with Choice Principles

This paper is concerned with metamathematical properties of intuitionistic set theories with choice principles. It is proved that the disjunction property, the numerical existence property, Church’s rule, and several other metamathematical properties hold true for constructive Zermelo–Fraenkel Set Theory and full intuitionistic Zermelo–Fraenkel augmented by any combination of the principles of countable choice, dependent choices, and the presentation axiom. Also Markov’s principle may be added.

H. Friedman: The disjunction property implies the numerical existence property. Pro-ceedings of the National Academy of Sciences of the United States of America 72 (1975) 2877-2878.MATHCrossRefGoogle Scholar